Continued fractions and orthogonal polynomials in several variables

2023/03/28 by Tomas Sauer, Yuan Xu, Sauer, Tomas +1
Computer Science · Mathematics · #41A21 #42C05 #65D15 #65D32 #Classical Analysis and ODEs (math.CA) #Coding theory and cryptography #FOS: Mathematics #Numerical Analysis (math.NA) #Polynomial and algebraic computation #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2303.16030

openalex publication_date 2023/03/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend the close interplay between continued fractions, orthogonal polynomials, and Gaussian quadrature rules to several variables in a special but natural setting which we characterize in terms of moment sequences. The crucial condition for the characterization is the commutativity of the multiplication operators on finite polynomial subspaces modulo an ideal. Moreover, starting from the orthogonal polynomials or the three-term recurrence, our method constructs a sequence of moment sequences that provides an approximation of the maximal order for recovering the moment sequence that defines the orthogonality.

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